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Is there such a thing as an NP-complete optimization (not decision) problem?

What is an example of an NP-complete optimization problem?

The decision versions of optimization problems are the ones in NP-complete. I can't think of any NP-hard optimizations that can be confirmed in polynomial time. I need verification/correction on this.

Thank you.

terra
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    Formally, no -- NP-completeness implies membership in NP, and NP formally contains only decision problems. Calling optimization problems "NP-hard" is a minor abuse of terminology. – David Eisenstat Apr 25 '22 at 20:09
  • There is a class called NP-equivalent problems which is a class of problems that are both NP-hard and NP-easy (i.e. there is a poly time reduction both from and to some NP-complete problem). Note an optimization problem can be reduced from and/or to a decision problem so there's no problem with optimisation problems being NP-equivalent. – n. m. could be an AI Apr 25 '22 at 20:29

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